CN105138849A - Reactive voltage control partitioning method based on AP clustering - Google Patents

Abstract

The invention discloses a reactive voltage control partitioning method based on AP clustering. The reactive voltage control partitioning method comprises the following steps that voltage reactive sensitivity is obtained based on a Jacobian matrix obtained through power flow calculation, and a PQ node electrical distance matrix is structured based on voltage sensitivity among PQ nodes; the minus of all elements of the PQ node electrical distance matrix is taken, and a similarity matrix is structured; the optimal clustering center, the optimal clustering number and a partitioning clustering result are obtained, and clustering of the PQ nodes is completed; the voltage regulating and control sensitivity of all PV nodes to all PQ partitions is calculated based on a perturbation method, and the PV nodes are partitioned into the PQ partition most sensitive in voltage regulating and control. The AP clustering algorithm is applied to voltage reactive partitions, the clustering number can be automatically obtained, unsupervised learning is carried out based on definitive evidence spreading, subjective factors in the clustering process are effectively reduced, the problem of random searching is effectively solved, and random factors are not included in the algorithm process.

Description

A kind of Power Network Partitioning method based on AP cluster

Technical field

The present invention relates to a kind of Power Network Partitioning method based on AP cluster.

Background technology

Grid nodes subregion is the basis of tertiary voltage control, and therefore effective partition method is voltage-controlled basic problem.Current partition method achievement in research comparatively horn of plenty, conventional voltage partition method can be summarized as following four classes: fuzzy clustering, graph theory, heuritic approach (as simulated annealing, tabu search etc.), learning method (as K-means).Existing method can be applicable to traditional electrical network preferably, but experience people need be relied on for specified partition number, therefore can increase the subjective factor in subregion process; When clustering algorithm starts simultaneously, its initial cluster center and the direction of search are to be determined at random, makes cluster result easily be absorbed in local optimum.

Summary of the invention

The present invention is in order to solve the problem, propose a kind of Power Network Partitioning method based on AP cluster, this method adopts advanced AP clustering algorithm as core partitioning algorithm, can overcome the artificial given problem of the number of partitions and algorithm starts stochastic problems thus avoids being absorbed in local optimum.

To achieve these goals, the present invention adopts following technical scheme:

Based on a Power Network Partitioning method for AP cluster, comprise the following steps:

(1) Jacobian matrix based on Load flow calculation gained obtains voltage power-less sensitivity, based on voltage sensitivity between PQ node, builds PQ node electrical distance matrix;

(2) each element of PQ node electrical distance matrix is got negative, build similarity matrix;

(3) iterations i is set, calculates the similarity between each PQ node and other PQ nodes and similarity evident information value, obtain each PQ node comprehensive similarity and responsivity value under i-th iteration;

(4) after judging successive ignition, whether each PQ node comprehensive similarity and responsivity value symbol are stablized constant or whether reach maximum iteration time, if so, step (5) is proceeded to, otherwise, by iterations cumulative 1, proceed to step (3);

(5) obtain optimum cluster mid point and clusters number, obtain subarea clustering result, complete PQ node clustering;

(6) each PV node is calculated to the region voltage in each PQ region regulation and control sensitivity based on perturbation method, by PV node division in the sensitiveest PQ subregion of its regulating and controlling voltage.

In described step (1), Newton-Raphson method is adopted to obtain following power flow equation:

$\left[\begin{array}{c}\mathrm{\Δ}P\\ \mathrm{\Δ}Q\end{array}\right]=\left[\begin{array}{cc}H& N\\ M& L\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}\mathrm{\θ}\\ \mathrm{\Δ}U\end{array}\right]---\left(1\right)$

Studying idle on ignoring meritorious change during the affecting of voltage, namely thinking and Δ P=0 now being obtained by formula (1): $\frac{\∂\mathrm{\Δ}U}{\∂\mathrm{\Δ}Q}={(L-{\mathrm{MH}}^{-1}N)}^{-1},$

Defining the internodal voltage power-less sensitivity of PQ is thus:

$\mathrm{\α}=\frac{\∂\mathrm{\Δ}U}{\∂\mathrm{\Δ}Q}={(L-{\mathrm{MH}}^{-1}N)}^{-1}---\left(2\right)$

Wherein: α is N*N square formation, N is PQ nodes, matrix arbitrary element α _ijrepresent that node i is to the voltage power-less sensitivity of node j, direct Jacobian matrix obtains voltage power-less sensitivity thus.

In described step (1), the PQ node being coupled strong by voltage influence divides to same district, and by Approximate Decoupling between node weak for coupling, between definition PQ node, voltage sensitivity is as follows:

${\mathrm{\β}}_{ij}=\frac{\∂U_i}{\∂U_j}=\frac{\∂U_i}{\∂Q_j}\·\frac{\∂Q_j}{\∂U_j}=\frac{{\mathrm{\α}}_{ij}}{{\mathrm{\α}}_{jj}}---\left(3\right)$

In formula, β _ijfor voltage sensitivity between node i and j, α _ijfor node i is to the voltage power-less sensitivity of node j, α _jjfor the idle sensitivity of node j its voltage.

In described step (1), obtain between PQ node after voltage sensitivity, the electrical distance between defined node is as follows:

D _ij＝lg(β _ij·β _ji)(4)

Wherein, D _ijrepresent the electrical distance between any two node i and j, form electrical distance matrix diagonals line element and set to 0, namely adopt similarity weight, electrical distance matrix D will form similarity matrix and input as algorithm.

In described step (2), based on the definition to electrical distance, carry out the structure of similarity matrix S, concrete grammar is: each element of electrical distance matrix gets negative value, can form similarity matrix S.

In described step (3), concrete grammar is: deflection parameter p (i) arranging similarity matrix, when without priori, each p (i) all gets S all elements intermediate value, this shows that AP clustering algorithm thinks the potential central point of the chances such as each node is when original state, in unmanned supervised learning process, R (i, k) be the evident information that all the other node i arbitrary are transmitted to candidate cluster center k, represent that k obtains from i point and support that it becomes the evidence size of cluster centre point; A (i, k) be evident information that candidate cluster center k transmits to all the other node i arbitrary, represent that k self is applicable to the evidence size of the cluster centre becoming i point, according to the R (i that candidate cluster central point k collected from all the other all nodes, k) with A (i, k) (i ≠ k) basic evident information obtains comprehensive fitness degree R (k, k) and comprehensive responsiveness A (k, k) two high-level information parameters of k node.

In described step (3), evidence transmission is undertaken by following formula:

R (i, k)=S (i, k)-max{A (i, k ')+S (i, k ') } (k ' ∈ 1,2 ..., N}, but k ' ≠ k) and (5)

$A(i,k)=min\{0,R(k,k)+{\mathrm{\Σ}}_{i^{\′}s.t.i^{\′}\∉\{i,k\}}max\{0,R(i^{\′},k)\left\}\right\}---\left(6\right)$

R (k, k)=P (k)-max{A (k, i ')+S (k, i ') } (i ' ∈ 1,2 ..., N}, but i ' ≠ k) and (7)

A(k，k)＝∑ _{i′s.t.i′≠k}max{0，R(i′，k)}(8)

In formula: S (i, k), S (i, k '), S (k, i ') is respectively the capable k column element of similarity matrix i, i capable k ' column element and k capable i ' column element; A (i, k ') and A (k, i ') is respectively the availability evident information value of node k ' to node i and node i ' transmit to node k; R (i ', k) for node i ' to node k transmit responsibility evident information value;

P (k) is the capable k column element of similarity matrix k; N is the whole network PQ nodes; The off-diagonal element of similarity matrix S is only relied on by the known evidence transmission of above formula; Start initial value and depend on deflection parameter p (i).

In described step (4), R (the k be once delivered to collected by each point in study, k) with A (k, k) by decision, whether it becomes cluster centre point to evident information, each point is competed according to determinacy evidence size, and finishing screen selects m high-quality cluster centre point, determines that cluster numbers is m simultaneously, non-cluster central point i sorts out to each contact Centroid the most closely with maximum similarity principle, and the whole network PQ partition of nodes completes.

In described step (6), concrete grammar comprises:

(6-1) all PV node voltages are set to reference voltage perunit value;

(6-2) Load flow calculation is carried out to the whole network, store the voltage perunit value of the PQ node in each region according to each PQ subregion respectively, and in this, as benchmark;

(6-3) PV node voltage perturbation upper lower limit value is set.Keep all the other PV node voltages constant, the voltage of change i-th the PV node that only perturb, the voltage that perturbation changes PV node i is VC (j);

(6-4) the whole network carries out Load flow calculation, stores the voltage perunit value of each PQ node in each region by each PQ subregion respectively, judges now whether j is greater than setting value, if so, then step (6-5) is proceeded to, if not, then return step (6-3), and j value is added 1;

(6-5) calculate PV node i when perturbing respectively as bound voltage, in PQ subregion each PQ node current voltage and benchmark state voltage deviation absolute value and average, it can be used as this PV node to the regulating and controlling voltage sensitivity of this PQ subregion;

(6-6) the regulating and controlling voltage sensitivity of each PV node to each PQ subregion is calculated successively, each subregion sensitivity is sorted, by PV node division in the PQ subregion of the maximum correspondence of region voltage regulation and control sensitivity, until all PV nodes all complete, each PV node is all divided in the sensitiveest PQ subregion of corresponding regulation and control.

In described step (6), definition PV node is to the regulating and controlling voltage sensitivity relation of PQ node:

F·ΔV _PV＝ΔV _PQ(9)

In formula, Δ V _pVwith Δ V _pQrepresent that PV node and PQ node voltage change respectively; F is sensitivity matrix, when a kth PV node voltage makes small perturbation Δ V _k, Load flow calculation obtains each PQ node voltage increment [Δ V _pQ1, Δ V _pQ2... Δ V _pQN], wherein N is PQ nodes, as Δ V _kwhen being less than setting value, desirable Δ V _k=0.01p.u., the regulating and controlling voltage sensitivity of a definition kth PV node to each PQ node is: perturbation method is utilized to obtain PV node to the regulating and controlling voltage sensitivity of arbitrary PQ node.

In described step (6), the original state of PV partition of nodes is m high-quality PQ subregion, need define the region voltage regulation and control sensitivity of single PV node to arbitrary PQ subregion, when in PQ subregion, maximum region nodes λ is less than threshold values λ _reftime pay the utmost attention to degree of accuracy, the definition sensitivity average of PV node to PQ node each in region is sensitivity; Otherwise λ is greater than threshold values λ _reftime, pay the utmost attention to calculated amount, the sensitivity of definition PV node to PQ subarea clustering center is sensitivity; λ _refit is fixed to get according to computing system capacity, and PV node definition is as follows:

${\mathrm{\&alpha;}}_h=\left\{\begin{array}{cc}\frac{1}{2n_h}\underset{t=1}{\overset{n_h}{\&Sigma;}}\left(\frac{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQt}}}{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}+\frac{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQt}}}{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}\right)& (\mathrm{\&lambda;}<{\mathrm{\&lambda;}}_{ref})\\ \frac{1}{2}\left(\frac{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQC}}}{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}+\frac{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQC}}}{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}\right)& (\mathrm{\&lambda;}\&GreaterEqual;{\mathrm{\&lambda;}}_{ref})\end{array}\right.---\left(10\right)$

Wherein: λ=max{n ₁, n ₂..., n _l; H is PQ zone number; n _hfor PQ nodes contained in the h of region; T is PQ node serial number; K is PV node serial number; C is the cluster centre PQ node number of PQ subregion h; L is the PQ number of partitions, α _hfor PV node k is to the voltage control sensitivity of region h.

In described step (6), adopt upwards downwards Perturbation Sensitivity average as overall sensitivity, wherein with represent PV node k upper voltage limit perturbation increment respectively, and the voltage increment of the corresponding generation of arbitrary PQ node t in h subregion; Δ V _k with Δ V _pQt represent PV node k lower voltage limit perturbation increment respectively, and the voltage increment of the corresponding generation of arbitrary PQ node t in h subregion; And the voltage increment of the corresponding generation of arbitrary PQ node t in h subregion; with Δ V _pQC represent that PV node k voltage is respectively to upper downward perturbation respectively and Δ V _k time, the voltage increment of the corresponding generation of cluster centre PQ point C in h subregion,

Form PV node k thus to each PQ partitioned area regulating and controlling voltage sensitivity vector: [α ₁, α ₂..., α _l].

Beneficial effect of the present invention is:

(1) AP clustering algorithm is applied to voltage power-less subregion and automatically can draws clusters number, and carry out unsupervised learning based on determinacy evidence propagation, subjective factor in effective minimizing cluster process, effectively solves random search problem, and algorithmic procedure is not containing enchancement factor;

(2) define PV node to the regulating and controlling voltage sensitivity of PQ subregion based on perturbation method, consideration PQ node is different from PV node response process, realizes subregion stage by stage, and regulating and controlling voltage sensitivity, with electrical distance close relation, shows to define validity;

(3) can ensure that PQ partition of nodes is connective, pass through phenomenon without node, each region reactive source Node distribution is even.

Accompanying drawing explanation

Fig. 1 is that PQ node of the present invention is based on AP cluster subregion process flow diagram;

Fig. 2 is that PV node of the present invention is based on preferential sensitivity subregion process flow diagram;

Fig. 3 is AP cluster result schematic diagram;

Fig. 4 is NewEngland39 node system block plan.

Embodiment:

Below in conjunction with accompanying drawing and embodiment, the invention will be further described.

1 based on the PQ partition of nodes of AP clustering algorithm

AP clustering algorithm is summarized

Current algorithm all needs artificial empirically prediction cluster numbers as algorithm input quantity, thus can increase the interference of cluster process subjectivity; Some algorithm will, based on the cluster centre of random selecting or the direction of search, make cluster result easily be absorbed in local optimum when starting in addition.

Based on above consideration, the present invention chooses more advanced affine propagation clustering algorithm (AP cluster) on clustering algorithm, and AP clustering algorithm is a kind of unmanned supervised learning method newly in recent years proposed.Algorithm only with domain euclidean distance between node pair matrix for input (distance matrix can also can be asymmetric battle array for symmetrical matrix), fast towards multi-site data cluster speed; During startup all data points all as etc. the cluster centre point of chance; Cluster process carries out unsupervised learning with deterministic evidence propagation and competes, and automatically draws Optimal cluster centers and corresponding cluster numbers and avoids artificially specifying in advance.Non-cluster central point is then sorted out extremely nearest central point with maximum similarity principle and is completed cluster.

In algorithm evidence propagation learning process, each candidate cluster central point and the whole network sample point carry out bi-directional responsibility and availability evident information.Responsibility is called responsiveness, is to be transmitted to candidate cluster central point by sample node to represent that sample point supports that this candidate cluster central point becomes the evidence size of cluster centre; Availability is called support, is to be transmitted to sample point by candidate cluster central point to represent that this candidate cluster center is suitable as the evidence size of the cluster centre of sample point.Evident information transmission relies on euclidean distance between node pair matrix completely, can realize unsupervised learning, thus cluster result objective and data network shelf structure is constant time result there is repeatability.

1.1 realize PQ partition of nodes based on AP cluster

1.1.1PQ node electrical distance matrix

Electrical distance directly determines division result and quality as contacting tight ness rating size figureofmerit between node in voltage partition.Electrical distance required for voltage partition should characterize voltage couples intensity between node, therefore can define with voltage power-less sensitivity.The method that Jacobian matrix based on Load flow calculation gained obtains voltage power-less sensitivity and then definition electrical distance has all been applied and has obtained good result in many documents.

Newton-Raphson method is adopted to obtain following power flow equation:

$\left[\begin{array}{c}\mathrm{\&Delta;}P\\ \mathrm{\&Delta;}Q\end{array}\right]=\left[\begin{array}{cc}H& N\\ M& L\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;}\mathrm{\&theta;}\\ \mathrm{\&Delta;}U\end{array}\right]---\left(1\right)$

Study and idlely ignoring meritorious change to being similar to during the affecting of voltage, namely think Δ P=0.Now can be obtained by formula (1): $\frac{\&part;\mathrm{\&Delta;}U}{\&part;\mathrm{\&Delta;}Q}={(L-{\mathrm{MH}}^{-1}N)}^{-1}$

Defining the internodal voltage power-less sensitivity of PQ is thus:

$\mathrm{\&alpha;}=\frac{\&part;\mathrm{\&Delta;}U}{\&part;\mathrm{\&Delta;}Q}={(L-{\mathrm{MH}}^{-1}N)}^{-1}---\left(2\right)$

Wherein: α is N*N square formation, N is PQ nodes.Matrix arbitrary element α _ijrepresent that node i is to the voltage power-less sensitivity of node j.Directly can obtain voltage power-less sensitivity with Jacobian matrix thus.

The PQ node that voltage influence is mainly coupled strong by subregion divides to same district, and by Approximate Decoupling between node weak for coupling.Thus based on voltage power-less sensitivity PQ node between voltage sensitivity more can intuitively reflect internodal coupling.Between definition PQ node, voltage sensitivity is as follows:

${\mathrm{\&beta;}}_{ij}=\frac{\&part;U_i}{\&part;U_j}=\frac{\&part;U_i}{\&part;Q_j}\&CenterDot;\frac{\&part;Q_j}{\&part;U_j}=\frac{{\mathrm{\&alpha;}}_{ij}}{{\mathrm{\&alpha;}}_{jj}}---\left(3\right)$

In formula, β _ijfor voltage sensitivity between node i and j, α _ijfor node i is to the voltage power-less sensitivity of node j, α _jifor the idle sensitivity of node j its voltage.

Obtain between PQ node after voltage sensitivity, just can electrical distance based on this between defined node.Definition electrical distance is as follows:

D _ij＝lg(β _ij·β _ji)(4)

Wherein, D _ijrepresent the electrical distance between any two node i and j.Form electrical distance matrix diagonals line element and set to 0, namely adopt similarity weight.

When application AP cluster realizes PQ partition of nodes, electrical distance matrix D will form similarity matrix and input as algorithm.

1.1.2PQ node clustering process

Utilize AP clustering algorithm to realize PQ node auto-partition, first should prepare similarity matrix S.Based on the above-mentioned definition to electrical distance, carry out the structure of similarity matrix S.Arrange deflection parameter p (i) of similarity matrix, when without priori, each p (i) all gets S all elements intermediate value, and this shows that AP clustering algorithm thinks the potential central point of the chances such as each node is when original state; In unmanned supervised learning process, the evident information that R (i, k) transmits to candidate cluster center k for all the other node i arbitrary, represents that k obtains from i point and supports that it becomes the evidence size of cluster centre point; The evident information that A (i, k) transmits to all the other node i arbitrary for candidate cluster center k, represents that k self is applicable to the evidence size of the cluster centre becoming i point.According to the R (i that candidate cluster central point k collected from all the other all nodes, k) with A (i, k) (i ≠ k) basic evident information obtains the comprehensive fitness degree R (k of k node, k) with comprehensive responsiveness A (k, k) two high-level information parameters.Evidence transmission is undertaken by following formula:

R(i，k)＝S(i，k)-max{A(i，k′)+S(i，k′)}

(k ' ∈ 1,2 ..., N}, but k ' ≠ k) and (5)

$A(i,k)=min\{0,R(k,k)+{\mathrm{\&Sigma;}}_{i^{\&prime;}s.t.i^{\&prime;}\&NotElement;\{i,k\}}max\{0,R(i^{\&prime;},k)\left\}\right\}---\left(6\right)$

R(k，k)＝P(k)-max{A(k，i′)+S(k，i′)}

(i ' ∈ 1,2 ..., N}, but i ' ≠ k) and (7)

A(k，k)＝∑ _{i′s.t.i′≠k}max{0，R(i′，k)}(8)

In formula: S (i, k), S (i, k '), S (k, i ') is respectively the capable k column element of similarity matrix i, i capable k ' column element and k capable i ' column element; A (i, k ') and A (k, i ') is respectively the availability evident information value of node k ' to node i and node i ' transmit to node k; R (i ', k) for node i ' to node k transmit responsibility evident information value;

P (k) is the capable k column element of similarity matrix k; N is the whole network PQ nodes; The off-diagonal element of similarity matrix S is only relied on by the known evidence transmission of above formula; Start initial value and depend on deflection parameter p (i) (diagonal element of S).

Whether it becomes cluster centre point by decision for the R (k, k) be once delivered to collected by each point in study and A (k, k) evident information, and each point is competed according to determinacy evidence size.Successively after study, the differentiation of competition difference expands and tends towards stability.Finishing screen is selected m high-quality cluster centre point and (is determined that cluster numbers is m) simultaneously.Non-cluster central point i sorts out to each contact Centroid the most closely with maximum similarity principle, and the whole network PQ partition of nodes completes.Process flow diagram as shown in Figure 1.

Next step, by the region voltage regulation and control sensitivity of each PV node of definition to each PQ subregion, obtains PV partition of nodes data encasement.

The 2 PV partition of nodes of sorting based on region voltage regulation and control sensitivity

After completing PQ partition of nodes, subregion classification need be carried out to PV node.Each subregion reactive source is evenly distributed and optimal voltage can be realized to control.Partitioned core object realizes PV node to sort out to the sensitiveest PQ region of its control.

2.1 perturbation method defined range regulating and controlling voltage sensitivity

Between node, voltage sensitivity affects by network parameter and operational factor, and PV node is to the regulating and controlling voltage sensitivity relation of PQ node:

F·ΔV _PV＝ΔV _PQ(9)

In formula, Δ V _pVwith Δ V _pQrepresent that PV node and PQ node voltage change respectively; F is sensitivity matrix.

The ultimate principle obtaining PV node voltage regulation and control sensitivity based on perturbation method is: when a kth PV node voltage makes small perturbation Δ V _k, Load flow calculation obtains each PQ node voltage increment [Δ V _pQ1, Δ V _pQ2... Δ V _pQN], wherein N is PQ nodes.As Δ V _ktime less, the regulating and controlling voltage sensitivity of a definition kth PV node to each PQ node can be: perturbation method is utilized to obtain PV node to the regulating and controlling voltage sensitivity of arbitrary PQ node.

The original state of PV partition of nodes is m high-quality PQ subregion, needs to define the region voltage regulation and control sensitivity of single PV node to arbitrary PQ subregion for this reason.The present invention is based on the dual consideration to degree of accuracy and calculated amount, when in PQ subregion, maximum region nodes λ is less than threshold values λ _reftime pay the utmost attention to degree of accuracy, the definition sensitivity average of PV node to PQ node each in region is sensitivity; Otherwise λ is greater than threshold values λ _reftime, pay the utmost attention to calculated amount, the sensitivity of definition PV node to PQ subarea clustering center is sensitivity; λ _refit is fixed to get according to computing system capacity.Be defined as follows:

${\mathrm{\&alpha;}}_h=\left\{\begin{array}{cc}\frac{1}{2n_h}\underset{t=1}{\overset{n_h}{\&Sigma;}}\left(\frac{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQt}}}{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}+\frac{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQt}}}{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}\right)& (\mathrm{\&lambda;}<{\mathrm{\&lambda;}}_{ref})\\ \frac{1}{2}\left(\frac{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQC}}}{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}+\frac{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQC}}}{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}\right)& (\mathrm{\&lambda;}\&GreaterEqual;{\mathrm{\&lambda;}}_{ref})\end{array}\right.---\left(10\right)$

Wherein: λ=max{n ₁, n ₂..., n _l; H is PQ zone number; n _hfor PQ nodes contained in the h of region; T is PQ node serial number; K is PV node serial number; C is the cluster centre PQ node number of PQ subregion h; L is the PQ number of partitions.α _hfor PV node k is to the voltage control sensitivity of region h.

For improving sensitivity accuracy, adopt upwards downwards Perturbation Sensitivity average as overall sensitivity.Wherein with represent PV node k upper voltage limit perturbation increment respectively, and the voltage increment of the corresponding generation of arbitrary PQ node t in h subregion; Δ V _k with point Δ V _pQt biao Shi PV node k lower voltage limit perturbation increment, and the voltage increment of the corresponding generation of arbitrary PQ node t in h subregion; And the voltage increment of the corresponding generation of arbitrary PQ node t in h subregion; with Δ V _pQC represent that PV node k voltage is respectively to upper downward perturbation respectively and Δ V _k time, the voltage increment of the corresponding generation of cluster centre PQ point C in h subregion.

Form PV node k thus to each PQ partitioned area sensitivity vector: [α ₁, α ₂..., α _l].

2.2PV partition of nodes

PV node is sorted to the sensitivity of each PQ subregion, this PV node is divided to the maximum PQ subregion of sensitivity, ensures its Control of Voltage greatest priority.So far two-stage subregion is completed.

Through carrying out subregion based on AP clustering algorithm to PQ node, then complete subregion based on voltage control sensitivity to PV node, the whole network partition of nodes completes.Implementation procedure as shown in Figure 2.

3 sample calculation analysis

Example adopts NewEngland39 node system, and wherein 1 to No. 29 node is PQ node; No. 31 nodes are balance node; All the other 10 nodes are PV node.

3.1 based on AP cluster PQ partition of nodes

Carry out the one-phase subregion based on AP clustering algorithm for system 29 PQ nodes, table 1 is depicted as this stage subarea clustering result.

29 PQ node division are 6 subregions by one-phase subregion, are 1 to 6 by its number consecutively, and division result represents the corresponding PQ node comprised in each subregion.According to NewEngland39 node topology figure, there is not reachability problem in cluster, and Area Node, without passing through phenomenon, shows Cluster Validity.And repeatedly repeating cluster, its result is constant.Show algorithm not containing enchancement factor and subjective factor.

Table 1 is based on AP cluster PQ node division result

3.2 sensitivity sequence PV partition of nodes

Consider that PQ node is different from PV node response process, complete that PQ node clustering is later calculates the voltage control sensitivity of each PV node to each PQ region based on perturbation method, and by PV node division in the sensitiveest PQ subregion of its Control of Voltage.

Table 2 is depicted as PV partition of nodes result, calculates the regulating and controlling voltage sensitivity of each PV node to each PQ subregion successively.The regulating and controlling voltage sensitivity of result display PV node to the PQ node region that it is directly connected is maximum, and when electrical distance is far away, sensitivity will reduce, and the rationality of the regulating and controlling voltage sensitivity that the present invention is based on perturbation method definition can be described.Each PV node voltage is selected to regulate and control the sensitiveest region as this partition of nodes.Result display PV partition of nodes, without passing through, ensures subregion connectedness and all there is reactive source node in each PQ subregion.

Table 2 is based on sensitivity sequence PV partition of nodes result

Existing method need travel through likely number of partitions subregion calculate corresponding index successively, thus calculated amount is large.The present invention adopts AP clustering algorithm, and without the need to specified partition number before subregion, algorithm self-adaptation can draw 6 division result, and calculated amount is minimum.Show the advantage of AP clustering algorithm in voltage power-less subregion and rationality thus.

In system, No. 31 nodes are balance node, and the present invention to the area principle that it adopts is: directly sort out to its PQ node place subregion be directly connected.So far, all partition of nodes of electrical network complete, and division result is as shown in table 3.

Table 3 the whole network division result

AP clustering algorithm is applied to voltage power-less subregion can draw clusters number automatically, and carries out unsupervised learning based on determinacy evidence propagation, effectively reduces subjective factor in cluster process.Repeatedly double counting, cluster result is constant, shows that algorithm effectively solves random search problem, and algorithmic procedure is not containing enchancement factor.

Based on perturbation method definition PV node to the regulating and controlling voltage sensitivity of PQ subregion, consideration PQ node is different from PV node response process, realizes subregion stage by stage.Regulating and controlling voltage sensitivity, with electrical distance close relation, shows to define validity.

Division result ensures subregion connectivity, and pass through phenomenon without node, each region reactive source Node distribution is even.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (10)

1., based on a Power Network Partitioning method for AP cluster, it is characterized in that: comprise the following steps:

(1) Jacobian matrix based on Load flow calculation gained obtains voltage power-less sensitivity, based on voltage sensitivity between PQ node, builds PQ node electrical distance matrix;

(2) each element of PQ node electrical distance matrix is got negative, build similarity matrix;

(3) iterations i is set, calculates the similarity between each PQ node and other PQ nodes and similarity evident information value, obtain each PQ node comprehensive similarity and responsivity value under i-th iteration;

(4) after judging successive ignition, whether each PQ node comprehensive similarity and responsivity value symbol are stablized constant or whether reach maximum iteration time, if so, step (5) is proceeded to, otherwise, by iterations cumulative 1, proceed to step (3);

(5) obtain optimum cluster mid point and clusters number, obtain subarea clustering result, complete PQ node clustering;

(6) each PV node is calculated to the region voltage in each PQ region regulation and control sensitivity based on perturbation method, by PV node division in the sensitiveest PQ subregion of its regulating and controlling voltage.

2. a kind of Power Network Partitioning method based on AP cluster as claimed in claim 1, is characterized in that: in described step (1), adopts Newton-Raphson method to obtain following power flow equation:

$\left[\begin{array}{c}\mathrm{\&Delta;}P\\ \mathrm{\&Delta;}Q\end{array}\right]=\left[\begin{array}{cc}H& N\\ M& L\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;}\mathrm{\&theta;}\\ \mathrm{\&Delta;}U\end{array}\right]---\left(1\right)$

Ignore meritorious change, namely think and Δ P=0 now obtained by formula (1):

Defining the internodal voltage power-less sensitivity of PQ is thus:

$\mathrm{\&alpha;}=\frac{\&part;\mathrm{\&Delta;}U}{\&part;\mathrm{\&Delta;}Q}={(L-{\mathrm{MH}}^{-1}N)}^{-1}---\left(2\right)$

Wherein: α is N*N square formation, N is PQ nodes, matrix arbitrary element α _ijrepresent that node i is to the voltage power-less sensitivity of node j, direct Jacobian matrix obtains voltage power-less sensitivity thus.

3. a kind of Power Network Partitioning method based on AP cluster as claimed in claim 1, it is characterized in that: in described step (1), the PQ node being coupled strong by voltage influence divides to same district, and by Approximate Decoupling between node weak for coupling, between definition PQ node, voltage sensitivity is as follows:

${\mathrm{\&beta;}}_{ij}=\frac{\&part;U_i}{\&part;U_j}=\frac{\&part;U_i}{\&part;Q_j}\&CenterDot;\frac{\&part;Q_j}{\&part;U_j}=\frac{{\mathrm{\&alpha;}}_{ij}}{{\mathrm{\&alpha;}}_{jj}}---\left(3\right)$

In formula, β _ijfor voltage sensitivity between node i and j, α _ijfor node i is to the voltage power-less sensitivity of node j, α _jjfor the idle sensitivity of node j its voltage.

4. a kind of Power Network Partitioning method based on AP cluster as claimed in claim 1, is characterized in that: in described step (1), and obtain between PQ node after voltage sensitivity, the electrical distance between defined node is as follows:

D _ij＝lg(β _ij·β _ji)(4)

Wherein, D _ijrepresent the electrical distance between any two node i and j, form electrical distance matrix diagonals line element and set to 0, namely adopt similarity weight, electrical distance matrix D will form similarity matrix and input as algorithm.

5. a kind of Power Network Partitioning method based on AP cluster as claimed in claim 1, it is characterized in that: in described step (3), concrete grammar is: deflection parameter p (i) arranging similarity matrix, when without priori, each p (i) all gets S all elements intermediate value, this shows that AP clustering algorithm thinks the potential central point of the chances such as each node is when original state, in unmanned supervised learning process, R (i, k) be evident information that all the other node i arbitrary are transmitted to candidate cluster center k, represent that k obtains from i point and support that it becomes the evidence size of cluster centre point, A (i, k) be evident information that candidate cluster center k transmits to all the other node i arbitrary, represent that k self is applicable to the evidence size of the cluster centre becoming i point, according to the R (i that candidate cluster central point k collected from all the other all nodes, k) with A (i, k) (i ≠ k) basic evident information obtains comprehensive fitness degree R (k, k) and comprehensive responsiveness A (k, k) two high-level information parameters of k node.

6. a kind of Power Network Partitioning method based on AP cluster as claimed in claim 1, is characterized in that: in described step (3), evidence transmission is undertaken by following formula:

R (i, k)=S (i, k)-max{A (i, k ')+S (i, k ') } (k ' ∈ 1,2 ..., N}, but k ' ≠ k) and (5)

$A(i,k)=min\{0,R(k,k)+{\mathrm{\&Sigma;}}_{i^{\&prime;}s.t.i^{\&prime;}\&NotElement;\{i,k\}}max\{0,R(i^{\&prime;},k)\left\}\right\}---\left(6\right)$

R (k, k)=P (k)-max{A (k, i ')+S (k, i ') } (i ' ∈ 1,2 ..., N}, but i ' ≠ k) and (7)

A(k，k)＝∑ _{i′s.t.i′≠k}max{0，R(i′，k)}(8)

In formula: S (i, k), S (i, k '), S (k, i ') is respectively the capable k column element of similarity matrix i, i capable k ' column element and k capable i ' column element; A (i, k ') and A (k, i ') is respectively the availability evident information value of node k ' to node i and node i ' transmit to node k; R (i ', k) for node i ' to node k transmit responsibility evident information value;

P (k) is the capable k column element of similarity matrix k; N is the whole network PQ nodes; The off-diagonal element of similarity matrix S is only relied on by the known evidence transmission of above formula; Start initial value and depend on deflection parameter p (i).

7. a kind of Power Network Partitioning method based on AP cluster as claimed in claim 1, it is characterized in that: in described step (4), R (the k be once delivered to collected by each point in study, k) with A (k, k) by decision, whether it becomes cluster centre point to evident information, each point is competed according to determinacy evidence size, finishing screen selects m high-quality cluster centre point, determine that cluster numbers is m simultaneously, non-cluster central point i sorts out to each contact Centroid the most closely with maximum similarity principle, and the whole network PQ partition of nodes completes.

8. a kind of Power Network Partitioning method based on AP cluster as claimed in claim 1, is characterized in that: in described step (6), concrete grammar comprises:

(6-1) all PV node voltages are set to reference voltage perunit value;

(6-2) Load flow calculation is carried out to the whole network, store the voltage perunit value of the PQ node in each region according to each PQ subregion respectively, and in this, as benchmark;

(6-3) PV node voltage perturbation upper lower limit value is set; Keep all the other PV node voltages constant, the voltage of change i-th the PV node that only perturb, the voltage that perturbation changes PV node i is VC (j);

(6-4) the whole network carries out Load flow calculation, stores the voltage perunit value of each PQ node in each region by each PQ subregion respectively, judges now whether j is greater than setting value, if so, then step (6-5) is proceeded to, if not, then return step (6-3), and j value is added 1;

(6-5) calculate PV node i when perturbing respectively as bound voltage, in PQ subregion a PQ node current voltage and benchmark state voltage deviation absolute value and average, it can be used as this PV node to the regulating and controlling voltage sensitivity of this PQ subregion;

(6-6) the regulating and controlling voltage sensitivity of each PV node to each PQ subregion is calculated successively, each subregion sensitivity is sorted, by PV node division in the PQ subregion of the maximum correspondence of sensitivity, until all PV nodes all complete, each PV node is all divided in the sensitiveest PQ subregion of corresponding regulation and control.

9. a kind of Power Network Partitioning method based on AP cluster as claimed in claim 1, is characterized in that: in described step (6), and definition PV node is to the regulating and controlling voltage sensitivity relation of PQ node:

F·ΔV _PV＝ΔV _PQ(9)

In formula, Δ V _pVwith Δ V _pQrepresent that PV node and PQ node voltage change respectively; F is sensitivity matrix, when a kth PV node voltage makes small perturbation Δ V _k, Load flow calculation obtains each PQ node voltage increment [Δ V _pQ1, Δ V _pQ2... Δ V _pQN], wherein N is PQ nodes, as Δ V _kwhen being less than setting value, the regulating and controlling voltage sensitivity of a definition kth PV node to each PQ node is: perturbation method is utilized to obtain PV node to the regulating and controlling voltage sensitivity of arbitrary PQ node.

10. a kind of Power Network Partitioning method based on AP cluster as claimed in claim 1, it is characterized in that: in described step (6), the original state of PV partition of nodes is m high-quality PQ subregion, the region voltage regulation and control sensitivity of single PV node to arbitrary PQ subregion need be defined, when in PQ subregion, maximum region nodes λ is less than threshold values λ _reftime pay the utmost attention to degree of accuracy, the definition sensitivity average of PV node to PQ node each in region is sensitivity; Otherwise λ is greater than threshold values λ _reftime, pay the utmost attention to calculated amount, the sensitivity of definition PV node to PQ subarea clustering center is sensitivity; λ _refit is fixed to get according to computing system capacity, and PV node definition is as follows:

${\mathrm{\&alpha;}}_h=\left\{\begin{array}{cc}\frac{1}{2n_h}\underset{t=1}{\overset{n_h}{\&Sigma;}}\left(\frac{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQt}}}{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}+\frac{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQt}}}{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}\right)& (\mathrm{\&lambda;}<{\mathrm{\&lambda;}}_{ref})\\ \frac{1}{2}\left(\frac{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQC}}}{\stackrel{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}+\frac{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_{PQC}}}{\underset{\&OverBar;}{{\mathrm{\&Delta;V}}_k}}\right)& (\mathrm{\&lambda;}\&GreaterEqual;{\mathrm{\&lambda;}}_{ref})\end{array}\right.---\left(10\right)$

Wherein: λ=max{n ₁, n ₂..., n _l; H is PQ zone number; n _hfor PQ nodes contained in the h of region; T is PQ node serial number; K is PV node serial number; C is the cluster centre PQ node number of PQ subregion h; L is the PQ number of partitions, α _hfor PV node k is to the voltage control sensitivity of region h; with represent PV node k upper voltage limit perturbation increment respectively, and the voltage increment of the corresponding generation of arbitrary PQ node t in h subregion; Δ V _k with point Δ V _pQt biao Shi PV node k lower voltage limit perturbation increment, and the voltage increment of the corresponding generation of arbitrary PQ node t in h subregion; And the voltage increment of the corresponding generation of arbitrary PQ node t in h subregion; with Δ V _pQC represent that PV node k voltage is respectively to upper downward perturbation respectively and Δ V _k time, the voltage increment of the corresponding generation of cluster centre PQ point C in h subregion, forms PV node k thus to each PQ partitioned area regulating and controlling voltage sensitivity vector: [α ₁, α ₂..., α _l].